Problem: A circle with circumference $18\pi$ has an arc with a $\dfrac{11}{9}\pi$ radians central angle. What is the length of the arc? ${18\pi}$ ${\dfrac{11}{9}\pi}$ $\color{#DF0030}{11\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{11}{9}\pi \div 2 \pi = \dfrac{s}{18\pi}$ $\dfrac{11}{18} = \dfrac{s}{18\pi}$ $\dfrac{11}{18} \times 18\pi = s$ $11\pi = s$